Decimals to Thousandths

The zeroes after a decimal point are useful clues. They show the place being discussed, so 0.4 and 0.400 can look different while naming the same amount.

Parents: let your child choose which decimal is greater before showing the place-value counters, then ask which denominator is allowed for a fraction conversion.

By the end you will be able to read decimals through thousandths, compare and order them, convert within the stated fraction boundary, and round to three accuracies.

Tenths, hundredths and thousandths

A decimal place names the size of a part: tenths, hundredths and thousandths. In 0.305, there are 3 tenths, 0 hundredths and 5 thousandths. Writing 0.350 keeps the zero thousandths place visible.

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Decimal places: build the value

🤔 Predict first: How many thousandths are in 0.305?

305 thousandths35 thousandths3 thousandths

Read 0.305 by place

$$0.305=3\text{ tenths}+0\text{ hundredths}+5\text{ thousandths}$$

$$0.305=\frac{305}{1000}$$

$$0.4=0.400$$

Compare and order decimals

Line up decimal places before comparing. First compare the tenths, then the hundredths, then the thousandths.

Show the worked solution

The aligned values show that 0.305 is less than 0.350, and 0.350 is the same value as 0.35.

Align the places

$$0.305=0.305$$

$$0.35=0.350$$

$$0.305<0.350$$

$$0.305<0.35$$

Decimal to fraction

The denominator records the place. A decimal through three places can be written over 10, 100 or 1,000. For 0.305, write 305 thousandths as $\frac{305}{1000}$. Keep the place-value fraction; simplify only when a question asks you to.

Write the denominator from the places

$$0.6=\frac{6}{10}$$

$$0.35=\frac{35}{100}$$

$$0.305=\frac{305}{1000}$$

Selected fractions to decimals

For this P4 conversion direction, use denominators that are factors of 10 or 100. Make an equivalent denominator of 10 or 100, then read the decimal. This gives $\frac{3}{5}$ = $\frac{6}{10}$ = 0.6 and $\frac{7}{20}$ = $\frac{35}{100}$ = 0.35. An unrestricted divide-top-by-bottom rule is outside this section.

Use an allowed denominator

$$\frac{3}{5}=\frac{6}{10}=0.6$$

$$\frac{7}{20}=\frac{35}{100}=0.35$$

$$\frac{3}{4}=\frac{75}{100}=0.75$$

Round decimals

To round, keep the named place and inspect the next digit. In 4.863, the next digit after the whole number is 8, the next after one decimal place is 6, and the next after two decimal places is 3.

One decimal, three accuracies

$$4.863\rightarrow5\text{ (nearest whole)}$$

$$4.863\rightarrow4.9\text{ (nearest 1 decimal place)}$$

$$4.863\rightarrow4.86\text{ (nearest 2 decimal places)}$$

Practise with worked steps

Practice 1. Represent 0.305 in tenths, hundredths and thousandths, then write it as a fraction.

Show the place-value solution

0.305

$$0.305=3\text{ tenths}+0\text{ hundredths}+5\text{ thousandths}$$

$$0.305=\frac{305}{1000}$$

Practice 2. Order 0.35, 0.305 and 0.4 from least to greatest. State the equal notation for 0.4.

Show the aligned comparison

Align to thousandths

$$0.305<0.350<0.400$$

$$0.35=0.350$$

$$0.4=0.400$$

Practice 3. Convert $\frac{3}{5}$ and $\frac{7}{20}$ to decimals, then round 4.863 to a whole number, 1 dp and 2 dp.

Show the conversion and rounding solution

Allowed conversions and rounding

$$\frac{3}{5}=\frac{6}{10}=0.6$$

$$\frac{7}{20}=\frac{35}{100}=0.35$$

$$4.863\rightarrow5,\;4.9,\;4.86$$

Watch out — easily mixed up

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

1. What is the value of the 5 in 0.305?

   5 tenths5 hundredths5 thousandths

2. Which comparison is true?

   0.305 > 0.350.305 < 0.350.305 = 0.35

3. Which fraction names 0.35?

   $\frac{35}{10}$$\frac{35}{100}$$\frac{35}{1000}$

4. Which fraction can be converted using an equivalent denominator of 100?

   $\frac{7}{20}$$\frac{1}{3}$$\frac{2}{7}$

5. What is 4.863 rounded to the nearest whole number?

   44.95

6. What is 4.863 rounded to 2 decimal places?

   4.864.874.8

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